So far as is known most small vises for fly tying, holding small parts for inspection, for assembly or for similar purposes are such that the clamping or gripping faces of the jaws do not remain parallel but tend to tilt more or less relative to each other depending upon the size of the work to be grasped. In the case of round objects particularly, especially curved round objects such as fish hooks, a great deal of force is thereby required to hold the object securely which often damages or even destroys the vise in relatively short time. It is thus the primary object of the present invention to provide a vise of the nature concerned, the gripping faces of whose jaws remain parallel throughout their travel.